48=8+5ln(4x+1)

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Solution for 48=8+5ln(4x+1) equation:


Simplifying
48 = 8 + 5ln(4x + 1)

Reorder the terms:
48 = 8 + 5ln(1 + 4x)
48 = 8 + (1 * 5ln + 4x * 5ln)
48 = 8 + (5ln + 20lnx)

Solving
48 = 8 + 5ln + 20lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-5ln' to each side of the equation.
48 + -5ln = 8 + 5ln + -5ln + 20lnx

Combine like terms: 5ln + -5ln = 0
48 + -5ln = 8 + 0 + 20lnx
48 + -5ln = 8 + 20lnx

Add '-20lnx' to each side of the equation.
48 + -5ln + -20lnx = 8 + 20lnx + -20lnx

Combine like terms: 20lnx + -20lnx = 0
48 + -5ln + -20lnx = 8 + 0
48 + -5ln + -20lnx = 8

Add '-48' to each side of the equation.
48 + -5ln + -48 + -20lnx = 8 + -48

Reorder the terms:
48 + -48 + -5ln + -20lnx = 8 + -48

Combine like terms: 48 + -48 = 0
0 + -5ln + -20lnx = 8 + -48
-5ln + -20lnx = 8 + -48

Combine like terms: 8 + -48 = -40
-5ln + -20lnx = -40

Reorder the terms:
40 + -5ln + -20lnx = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -5ln + -20lnx = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + -1ln + -4lnx) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(8 + -1ln + -4lnx)' equal to zero and attempt to solve: Simplifying 8 + -1ln + -4lnx = 0 Solving 8 + -1ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -1ln + -8 + -4lnx = 0 + -8 Reorder the terms: 8 + -8 + -1ln + -4lnx = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1ln + -4lnx = 0 + -8 -1ln + -4lnx = 0 + -8 Combine like terms: 0 + -8 = -8 -1ln + -4lnx = -8 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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